No this is not an odd response. A lot of Americans might say this. It's just very informal and it means that he/she is glad to help at any time. But I would write it as 2 words, any time
Formally, just say "You're welcome" or "Don't mention it" but you only need to say one of those in the most formal circumstances, as a sign of respect; for example, if you don't know someone, or if you're speaking to a business executive or someone who is much older than you.
I've found that "Any time" as a reply carries a certain tone of familiarity, in addition to being casual. Of course it can depend on whether one stresses the first word or the second. When said casually to a stranger, it implies, "Let's do it again sometime." (At least that's the way it seems to me.) [6] When it's said to a friend, there's usually no double meaning.